Resource allocations with guaranteed awards in claims problems
Giménez-Gómez, José Manuel , Peris, J.E. and Solís Baltodano, M.J. (2022) "Resource allocations with guaranteed awards in claims problems", Review of Economic Design
The notion of lower bound on awards has been introduced in the literature to analyze the establishment of guarantees that ensure a minimum award to each agent involved in situations of conflicting claims, such as the rationing of a resource or the distribution of the assets of a bankrupt firm. Indeed, this concept has a core role in many approaches related to the problem of fair allocation (Thomson in Math Soc Sci 74:41-59, 2015) and a range of such lower bounds have been proposed: the minimal right (Curiel et al. in Z Oper Res 31:A143-A159, 1987), the fair bound (Moulin in Handb Soc Choice Welf 1:289-357, 2002), securement (Moreno-Ternero and Villar in Math Soc Sci 47(2):245-257, 2004) and the min bound (Dominguez in mimeo, 2006). In this context, the key contribution of the current paper is to show that there is a correspondence between lower bounds and rules; i.e., associated to each particular lower bound, we find a specific way of distributing the resources. In doing so, we provide new characterizations for two well known rules, the constrained equal awards and Ibn Ezra's rules. A dual analysis, by using upper bounds on awards will provide characterizations of the dual of the previously mentioned rules: the constrained equal losses rule and the dual of Ibn Ezra's rule.